Importantly,

Boolean algebra enabled mathematicians to perform algebraic operations on symbols that represented units traditionally not regarded as mathematical objects.

The following lemma, due to Song and Kang [10], characterize invertible linear operators preserveing commuting pairs of matrices over a binary

Boolean algebra.

is the order complex of a rank selection of the

Boolean algebra [B.

1,0) is any

Boolean algebra, then there is a set X such that B is isomorphic to a Guard algebra on X.

Combining this with the facts that the

Boolean algebra is such a lattice and that homotopy Cohen-Macaulayness is implied by shellability, immediately yields the following.

This book also explores how genetics and

Boolean algebra will eventually have a greater impact on written and spoken thought processes, with the author employing examples of logic and language from both ancient Egyptian and modern tongues.

An extensive review of

Boolean algebra and logic gates is included.

Appendix A1 - Logic Gates And

Boolean Algebra In The Book

Topics covered include

Boolean algebra, combinational and sequential logic procedures, registers, a/d and d/a conversion, counters, and the logic family, among others.

The book starts with a full introduction to the basic principles behind digital systems, including chapters on logic gates and families,

Boolean algebra and minimization techniques.

Founded in 1967 and named after two 19th Century forerunners to the modern computing industry (George Boole -- of

Boolean algebra and Charles Babbage -- the Babbage Computing Machine) the Company today is the oldest publicly-traded independent software vendor in the systems management industry with revenues of $226 million in calendar 1998, 970 employees and 43 offices in 26 countries.

makes good use of his decades of experience as he focuses on the practical aspects of creating state machines while giving readers sufficient theory to understand what they are doing, starting by reviewing combinational logic, including number systems, number representations,

Boolean algebra, minimization, logic symbols, analysis and synthesis of combinational logic, multiplexers, decoders, encoders, comparators, storage elements, and programmable logic devices.